Consider an intersection of two one-way streets controlled by a traffic light. Assume that between 5 and 15 cars (varying probabilistically) arrive at the intersection every 10 sec in direction 1, and that between 6 and 24 cars arrive every 10 sec going in direction 2.
Suppose that 36 cars per 10 sec can cross the intersection in direction 1 and that 20 cars per 10 sec can cross the intersection in direction 2 if the traffic light is green. No turning is allowed. Initially, assume that the traffic light is green for 30 sec and red for 70 sec indirection 1. Write a simulation algorithm to answer the following questions for a 60-min time period:

a. How many cars pass through the intersection in direction 1 during the hour?

b. What is the average waiting time of a car stopped when the traffic signal is red in direction 1? The maximum waiting time?

c. What is the average length of the queue of cars stopped for a red light in direction 1? The maximum length?

d. What is the average number of cars passing through the intersection in direction 1 during the time when the traffic light is green? What is the maximum number?

e. Answer Problems (a)-(d) for direction 2.

How would you use your simulation to determine the switching period for which the total waiting time in both directions is as small as possible? (You will have to modify it to account for the waiting times in direction 2.)